Analysis of decoders for convolutional codes by stochastic sequential machine methods

In this paper, the decoder of a convolutional code is modeled as an autonomous stochastic sequential machine and finite Markov chain theory applied to obtain a precise expression for
P_{FD} (u)
, the probability of error associated with the feedback decoding of the
u
th subblock of information digits. The analysis technique developed extends directly to any convolutional decoder for a linear convolutional code, used for transmission over a finite state channel. The limit of
P_{FD} (u)
as
u
tends to infinity, when the limit exists, is termed
P_{FD}
, the steady-state probability of error of feedback decoding. Sufficient conditions on decoders are given in order for
P_{FD}
to exist, and two classes of minimum-distance decoders exhibited that meet these sufficient conditions.
P_{FD}
is calculated for an example using the binary-symmetric channel and found to satisfy
P_{FD} \le P_{DD}
where
P_{DD}
is the probability of error associated with feedback-free decoding of the same code.